/src/moddable/xs/tools/fdlibm/e_cosh.c
Line | Count | Source |
1 | | |
2 | | /* |
3 | | * ==================================================== |
4 | | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
5 | | * |
6 | | * Developed at SunSoft, a Sun Microsystems, Inc. business. |
7 | | * Permission to use, copy, modify, and distribute this |
8 | | * software is freely granted, provided that this notice |
9 | | * is preserved. |
10 | | * ==================================================== |
11 | | */ |
12 | | |
13 | | /* cosh(x) |
14 | | * Method : |
15 | | * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2 |
16 | | * 1. Replace x by |x| (cosh(x) = cosh(-x)). |
17 | | * 2. |
18 | | * [ exp(x) - 1 ]^2 |
19 | | * 0 <= x <= ln2/2 : cosh(x) := 1 + ------------------- |
20 | | * 2*exp(x) |
21 | | * |
22 | | * exp(x) + 1/exp(x) |
23 | | * ln2/2 <= x <= 22 : cosh(x) := ------------------- |
24 | | * 2 |
25 | | * 22 <= x <= lnovft : cosh(x) := exp(x)/2 |
26 | | * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2) |
27 | | * ln2ovft < x : cosh(x) := huge*huge (overflow) |
28 | | * |
29 | | * Special cases: |
30 | | * cosh(x) is |x| if x is +INF, -INF, or NaN. |
31 | | * only cosh(0)=1 is exact for finite x. |
32 | | */ |
33 | | |
34 | | #include "math_private.h" |
35 | | |
36 | | static const double one = 1.0, half=0.5, huge = 1.0e300; |
37 | | |
38 | | double |
39 | | __ieee754_cosh(double x) |
40 | 10.5k | { |
41 | 10.5k | double t,w; |
42 | 10.5k | int32_t ix; |
43 | | |
44 | | /* High word of |x|. */ |
45 | 10.5k | GET_HIGH_WORD(ix,x); |
46 | 10.5k | ix &= 0x7fffffff; |
47 | | |
48 | | /* x is INF or NaN */ |
49 | 10.5k | if(ix>=0x7ff00000) return x*x; |
50 | | |
51 | | /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ |
52 | 9.91k | if(ix<0x3fd62e43) { |
53 | 2.83k | t = s_expm1(fabs(x)); |
54 | 2.83k | w = one+t; |
55 | 2.83k | if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */ |
56 | 2.54k | return one+(t*t)/(w+w); |
57 | 2.83k | } |
58 | | |
59 | | /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ |
60 | 7.07k | if (ix < 0x40360000) { |
61 | 1.82k | t = __ieee754_exp(fabs(x)); |
62 | 1.82k | return half*t+half/t; |
63 | 1.82k | } |
64 | | |
65 | | /* |x| in [22, log(maxdouble)] return half*exp(|x|) */ |
66 | 5.25k | if (ix < 0x40862E42) return half*__ieee754_exp(fabs(x)); |
67 | | |
68 | | /* |x| in [log(maxdouble), overflowthresold] */ |
69 | 2.92k | if (ix<=0x408633CE) |
70 | 2 | return __ldexp_exp(fabs(x), -1); |
71 | | |
72 | | /* |x| > overflowthresold, cosh(x) overflow */ |
73 | 2.92k | return huge*huge; |
74 | 2.92k | } |